I really can't prove that the war was legal; others might, but the closest I could argue would be based around the use of the phrase "final opportunity to comply" in UNSC Resolution 1441. But many statements read into the record contradict that the resolution was intended to authorize a war. And both Bush and Blair may have had hopes of getting a war authorized by the UNSC after the fact, which is sort of what happened with UNSC Resolution 84 in 1950, after the USA had sent the 24th Infantry Division, which was occupying Japan, to the Korean peninsula, possibly exceeding UNSC Resolution 82, meaning they were "illegally" at war for a week.

What never gets pointed out is that if Blair is regarded as a criminal in this matter, history starts to look very different. General Galtieri after the Falklands and Saddam, after 1991, would have been tried. Medvedev, if not Putin (who gets it later for Crimea), would have over Georgia in 2008, and so would Brezhnev over Afghanistan. Soviet troops acting on Khrushchev's orders killed 4,000 Hungarian civilians in 1956. None of these were ever prosecuted by the ICC, but I realize I'm not putting Blair in the best company here, so I'll throw out more names.

We're also putting Anthony Eden, over Suez in 1956, in the dock, along with every Israeli leader since 1967, since the UN considers them to be illegally occupying East Jerusalem. George H.W. Bush over Panama in 1989 (although self-defense was claimed there because Noriega was suspected of involvement with smuggling drugs into the United States). Every Turkish leader since 1974 over Cyprus. Lyndon Johnson does, if not over Vietnam, then over the intervention in the Dominican Republic in 1965. Plus a good number of the leaders of India and Pakistan also get done for "aggression."

TL; DR: There is a bit of a "big country" bias in regards to what makes someone a "war criminal." And if you're the leader of a less developed country, life's a lot easier if you're allied with a country that has a Security Council veto.